MathematicsChapter 6: Permutation and Combination
Objects Kept Together in Arrangements
n people, 2 must be together: treat the pair as one, so (n-1)!
Learning objectives
- State the rule or meaning of objects kept together in arrangements in easy words.
- Apply objects kept together in arrangements in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
n people, 2 must be together: treat the pair as one, so (n-1)! * 2 (the pair can swap). Three together: 3! inside the block.
Where / symbols
- OBJECTS KEPT TOGETHER IN ARRANGEMENTS
- n people, 2 must be together: treat the pair as one, so (n-1)! * 2 (the pair can swap). Three together: 3! inside the block.
- TOGETHER
- n people, 2 must be together: treat the pair as one, so (n-1)!
Overview
Understand the idea, then apply it:
Main Idea
n people, 2 must be together: treat the pair as one, so (n-1)! * 2 (the pair can swap). Three together: 3! inside the block.
Examples 2! for a pair · (n-1)! blocks · Word: vowels as a block
Exam Use
Write the rule first: n people, 2 must be together: treat the pair as one, so (n-1)! Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Examples State the central idea · Use one accurate detail · Check the final response
WHAT — OBJECTS KEPT TOGETHER IN ARRANGEMENTS
n people, 2 must be together: treat the pair as one, so (n-1)! * 2 (the pair can swap). Three together: 3! inside the block.
WHY — Why it matters
This rule is a separate learning unit inside restrictions in arrangements. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: n people, 2 must be together: treat the pair as one, so (n-1)! Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a objects kept together in arrangements question
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
In simple words
Together uses a block. Not together is usually total minus together, not a new guess.
Key points
- block + inside
- together: glue as one super person
- not together: all - together
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Objects Kept Together in Arrangements
Sticky Notes · Quick Revision
Core Idea
- n people, 2 must be together: treat the pair as one, so (n-1)!
What to Know
- n people, 2 must be together: treat the pair as one, so (n-1)! * 2 (the pair can swap). Three together: 3! inside the block.
Example or Evidence
- 2! for a pair
- (n-1)! blocks
- Word: vowels as a block
How to Answer
- Write the rule first: n people, 2 must be together: treat the pair as one, so (n-1)! Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- Together uses a block. Not together is usually total minus together, not a new guess.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- n people, 2 must be together: treat the pair as one, so (n-1)!
- 2! for a pair
- (n-1)! blocks
- State the rule, show the working, and check the answer.
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